Next to the Intel Graphics Card there is also a NVIDIA GeForce GTX 850M, but the system tells me that there is no additional driver and installing nvidia-current breaks the display but this is not my main focus so just an additional information about my system. WLAN is much important.

Your card needed Ath10k module, information is here .
But , there is no backport for kernel 3.13. You can see available backport here.

Note : this method maybe not success and can breaking your installation. I didn't recommended it. The safe way is purchase a cheap wireless usb adapter who works in kernel 3.13 and wait until ath10k is back ported in ubuntu repo. . Last time i use backport a years ago and it give me a headache.

Open update manager and select view>linux kernel , drop down a list and select the latest kernel possible ( at this time is 3.16.0-31 ) and press install the 3.16.0.-31 and reboot . You can check the kernel in use with terminal command :

but I already did those steps in the exactly same way. So the support will be there in kernel 3.20, hope it will be possible to use it with the current mint version. Or I have to wait till a version which uses this kernel.

I think the Linux kernel version will be 4.0 instead of 3.20 and this is from the patch that will enable your device

The QCA6174 in combination with new wmi-tlv firmware is capable of
multi-channel, beamforming, tdls and other features.

This patch just makes it possible to boot these devices and do some basic stuff
like connect to an AP without encryption. Some things may not work or may be
unreliable. New features will be implemented later. This will be addressed
eventually with future patches.